OIS Chapter 3, Jaynes, Grammar of Graphics
2025-09-16
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What is available in the environment?
Two rules:
There are three common sources of probabilities:
The probability of a given integer on a k-sided die: \frac{1}{k}.
The probability of heads with a fair coin: \frac{1}{2}.
The probability of a Queen? \frac{4}{52}
The probability of a Diamond? \frac{13}{52}
The Queen of Diamonds? \frac{1}{52} or (\frac{4}{52}\times\frac{13}{52})
Quasirandom numbers
How often does something happen?
How likely am I to be admitted? Consult the admissions rate
How fast do I drive? Likelihood of law enforcement and need for speed
In data: this is tables.
No Yes
Female 0.6964578 0.3035422
Male 0.5548123 0.4451877
No Yes
Female 0.4612053 0.3173789
Male 0.5387947 0.6826211
No Yes
Female 0.2823685 0.1230667
Male 0.3298719 0.2646929
M.F No Yes
Female 0.6964578 0.3035422
Male 0.5548123 0.4451877
M.F No Yes
Female 0.4612053 0.3173789
Male 0.5387947 0.6826211
M.F No Yes
Female 0.2823685 0.1230667
Male 0.3298719 0.2646929
How likely do we believe something is?
Empirical frequency vs. subjective belief
What matters in group decision making is probably as much the beliefs [subjective] as the evidence [frequency].
How should we reflect this in strategies of argumentation/persuasion?
What matters?
The table sums to one.
For Berkeley:
The row/column sums to one. We collapse the table to a single margin. Here, two can be identified. The probability of Admit and the probability of M.F.
How does one margin of the table break down given values of another? Each row or column sums to one
Four can be identified, the probability of admission/rejection for Male, for Female; the probability of male or female for admits/rejects.
For Berkeley:
Is a combination of the distributive property of multiplication and the fact that probabilities sum to one.
For example, the probability of Admitted and Male is the probability of admission for males times the probability of male.
Pr(x=x, y=y) = Pr(y | x)Pr(x)
Or it is the probability of being admitted times the probabilty of being male among admits.
Pr(x=x, y=y) = Pr(x | y)Pr(y)
To find the joint probability [the intersection] of x and y, we can use either of the aforementioned methods. To turn this into a conditional probability, we simply take it is a proportion of the relevant margin.
Pr(x | y) = \frac{Pr(y | x) Pr(x)}{Pr(y)}
DADM-Fall 2025